AHU-0033 — Supply air temperature tracking error

Preconditions (host-enforced): Supply fan running and the unit occupied — a supply temperature describes nothing in still air, and an unoccupied unit is not chasing a setpoint. The unit must be in one of the four defined occupied modes, which APAR derives from the coil-valve and damper commands exactly the way this library derives its operating states, and the host must suspend evaluation for the usual ModeDelay (30 min) after any mode or operating-state change, plus through morning warmup and cooldown. That gate matters more here than on AHU-0007 or AHU-0013: this rule carries no actuator conjunct, so nothing inside it distinguishes a unit still stroking toward a new mode from a unit that cannot hold setpoint. sat_sp must be the setpoint the sequence is actively holding, reset included; bind a design constant against a unit that follows a reset schedule and the rule reports a fault every hour of every day. SAT sensor integrity is a precondition, not a conclusion — a sensor reading 2 K off produces a permanent tracking error at a perfectly tuned loop, and this rule reads no second signal that could tell the two apart, so clear whatever sensor-health rule the host runs on sat before believing the verdict. The rule discards the sign of the miss; a host that wants the direction reads sat and sat_sp alongside the verdict. When any gate is unmet the verdict is NO_EVAL, not healthy.

Points: sat, sat_sp

Outputs:

• yFault — True while |sat − sat_sp| has stayed above sat_error_threshold for at least alarm_delay. The only output — nothing in this rule is unevaluable from its own two inputs, so there is no evaluability flag and a host must not read one into it

Parameters:

Description

The supply air is not at its setpoint, and no actuator is at its stop. That second half is what makes this rule worth having separately. A loop whose valve has saturated is the easy case — the controller has asked for everything it has and the air is still wrong — and AHU-0007 and AHU-0013 state it, one per coil. A loop sitting 3 K off setpoint with its valve modulating around 60% is the harder case: the controller is not out of capacity, it is out of tune, or its valve has no authority left, or its actuator does not move until the ask gets large. Both sibling cards test the valve command first, so neither can ever report it. APAR states this as rule 25 and groups it with rules 3, 13 and 19 as comfort sacrificed, only the other three additionally establishing that the loop has run out of control authority. The fault is quiet by nature: zones compensate, boxes open, reheat picks up, and nobody files a ticket about a supply temperature.

Detection Logic

APAR rule 25, applicable in every defined occupied mode:

    | Tsa − Tsa,s | > εt          εt = 1.7 °C (3 °F)

as implemented:

    sp_gap = sat − sat_sp
    yFault = (|sp_gap| > sat_error_threshold), sustained continuously for alarm_delay

Block graph (rule.cxf.jsonld):

Four blocks, the same shape AHU-0010 uses for its equality test: spGap subtracts the setpoint from the measurement, absGap folds the two signs together, gapBig compares the magnitude against sat_error_threshold, and persist requires 60 continuous minutes before reporting. There is no fifth block, and the absence is the whole point of the card: every other SAT rule in this library carries a second conjunct — a saturated valve on AHU-0007 and AHU-0013, a reheat fraction on AHU-0019, a baseline on AHU-0022 — and each conjunct is what makes its rule specific and also what makes it blind. Rule 25 buys generality by spending specificity: it says the unit is not delivering what it was asked for and nothing at all about why. Persistence and the host’s mode gate are the only things keeping that statement from being noise, which is why both are set conservatively; delayOnInit = true holds the hour across a controller restart. gapBig is strict, as the source’s rule 25 is, so a miss sitting exactly on 1.7 K reads healthy — though exact equality is not reachable in doubles from a realistic temperature pair (see Deviations).

Possible Diagnoses

APAR names no per-rule causes; §4.2.2’s fault classes read through rule 25 and ordered by what an ungated tracking test finds first:

1. Control-loop tuning — a wide proportional band, a slow integral term, or a loop detuned to stop it hunting and left parked off setpoint since
2. Valve or damper authority: a valve sized to pass design flow at 20% open has no resolution left around setpoint
3. Actuator stiction, hysteresis, or a slipping linkage — the actuator does move, eventually, and never quite enough (AHU-0020 catches the frank case)
4. Coil or plant capacity short of saturation: degraded enough to miss setpoint, not enough to drive the valve to its stop, so the gated cards stay silent
5. Sequencing logic errors — a reset stepping faster than the unit can follow, two sequences writing the same coil output, a changeover leaving the unit on the previous mode’s setpoint
6. SAT sensor error: the air is at setpoint and the reading is not. Cheapest to rule out, and the reason sensor health is a precondition here
7. Operator intervention — a valve in hand, a coil output overridden (AHU-0027 reports the override directly)
8. A coil fighting the other coil: simultaneous heating and cooling holds SAT off setpoint at part-open commands, which AHU-0016 names

Energy Impact

COMFORT_ENERGY, MEDIUM confidence, PROXY_ESTIMATION. The category follows the source: rule 25 is in APAR’s comfort-requirements group, and what it establishes first is that the building is not getting the air it asked for. The runtime estimate is therefore an imbalance rather than a waste — imbalance_kw = supply_airflow_m3s × 1.2 × 1.005 × |sat − sat_sp|, host-supplied airflow — and the sign decides whether it is money: air colder than a cooling setpoint is over-cooling paid once at the coil and often again at terminal reheat, air warmer is under-delivery whose cost migrates downstream to boxes at maximum flow. Both invert in heating. No savings range is published; the reference’s 2–5% belongs to the saturated-coil siblings, so treat it as a ceiling. MEDIUM because the cause — which decides the cost and even its sign — is not in the rule’s two inputs. Climate-neutral.

Emissions Impact

PROXY_EMISSIONS, MEDIUM confidence. Scope is 1|2 because the rule spans every occupied mode and cannot tell which coil is involved: a heating-side miss made up by a gas boiler or steam coil is scope 1, while a cooling-side miss, electric heating, and the fan energy moving make-up air are scope 2. Basis: static combustion factor for the fuel half, MOER for the electric half. As on AHU-0013, fixing an under-delivery instance can raise site emissions — a loop that finally holds setpoint delivers conditioning the building was going without — so the claim that survives is the over-conditioning branch plus whatever downstream compensation stops.

Deviations

• This card is a library extension, not a transcription: the reference’s §5.8.1 index ends at AHU-0031. The detection logic is APAR rule 25 (§4.2 Table 1) with its threshold from §4.2.3; severity, phase, energy and emissions grades, persistence, the diagnosis list and the prose are authored here. The source report is personally licensed and not redistributed with this library.
• The valve-position gate is absent on purpose, and that absence is the card. APAR pairs a SAT miss with a saturated coil in rules 3, 13 and 19 and states rule 25 with the temperature term alone. AHU-0007 and AHU-0013 argue that a SAT miss at a part-open valve is a loop working through a load change — right for a rule that fires in half an hour, wrong as a general claim, since a loop 30 minutes or six months off setpoint at 60% command is working through nothing. This rule takes the other half of the trade and pays with a longer persistence and a stricter host gate.
• The overlap with AHU-0007 and AHU-0013 is real and not suppressed: a saturated valve missing setpoint trips this rule too, an hour later. The two findings are different statements and the gated one is more informative when both are true, so a host wanting one alarm should rank rather than silence.
• εt = 1.7 °C ships flat as the source states it, not composed. The G36-lineage cards here do compose their bands (AHU-0010 in quadrature, AHU-0005 linearly), so this is a departure from local practice in favour of source fidelity — and the honest reading, since the band must absorb sensor error and the tracking error a healthy proportional loop shows at partial load, of which only the first half has a published budget.
• sat_error_threshold shares its name with AHU-0007 and AHU-0013 but not its value or meaning: 1.0 °C there (G36’s eSAT, one-sided), 1.7 °C here (APAR’s εt, two-sided). The shared name keeps one vocabulary for “how far SAT may stray”; the parameter description states the difference so nobody copies a value across.
• alarm_delay = 3600 s is library-chosen; APAR states no persistence. Its §4.3 implementation evaluated rules on hourly data, and an hour matches this chapter’s other chronic conditions. It doubles the siblings’ 30 minutes because their second conjunct is rare enough that most transients never reach their timer, whereas here the timer is the only defence.
• No boundary rewrite: rule 25 is already strict, unlike the G36 ≥ the sibling cards convert. Exact equality is also unreachable — the double nearest 1.7 needs mantissa bits down to 2⁻⁵² and a difference of two temperatures in the 8–16 binade is a multiple of 2⁻⁴⁹ — so the vectors bracket the line instead of landing on it. Same class of finding as HW-0004’s 5.55 K trip line.
• Mode scope follows the source’s Table 2 (Modes 1–4), not Table 1’s “all occupied modes” heading, which would include APAR’s unknown mode. That is where the report puts mode transitions and simultaneous heating and cooling, and a SAT miss there is already reported with its cause attached by AHU-0016 and AHU-0029. A host can widen the gate.
• Mode gating is host-side, and the source agrees: APAR classifies its five modes from coil-valve and damper signals alone, then evaluates only the applicable rules — this library’s operating_states plus preconditions convention, reached independently two decades earlier. A verdict produced outside the four modes, in a transition window, or with the fan off is NO_EVAL and never healthy.
• Instantaneous samples against an hourly source. An hourly average tolerates a signal that keeps crossing back while its mean stays outside the band; persistence does not, so SAT oscillating across the band never alarms here. That case is AHU-0022’s to report, which is the reason to deploy both.
• The sign of the miss is computed and then discarded, because the source’s expression is a magnitude. Exposing it would add a block and an output to a rule whose value is its bluntness, and a host holding sat and sat_sp has the sign for free. Same treatment as AHU-0010.
• outputs carries yFault alone: every evaluability question this rule has — occupancy, mode, fan status, whether the setpoint is live, whether the SAT sensor is trustworthy — needs a signal the rule does not bind, so all of them are preconditions and none qualifies for a y…Ok output.
• Severity 3, phase 2 and the energy block are library-assigned; no reference row exists to copy. Severity 3 matches every comparison rule in this chapter, and savings_range declines to invent a number.
• APAR publishes an expression and a threshold, not test cases, so every scenario in vectors.json is authored.
• persist.delayOnInit = true (the CDL default is false), the library’s standing choice: a miss already present at load waits out the full hour rather than alarming on the first tick after a controller restart.
• playbooks, clusters and both suppression lists are empty. playbooks/ has no loop-tuning or coil-capacity playbook, which is what the first four diagnoses dispatch, and sensor-drift and missing-reset each cover one diagnosis apiece — listing them would over-claim. Cluster membership is arguable but is the index owner’s edit, not this card’s.

Notes

Read this card as the complement to AHU-0007 and AHU-0013, not a replacement. The three partition the SAT-miss space by what the actuator is doing: those two cover the saturated end, where the diagnosis list is short and the fix is usually mechanical, this one everything below saturation, where the list is long and the fix is usually at a keyboard. Tripping alone, it is a tuning, authority, or sequence problem until proven otherwise; tripping with one of the gated pair, it is repeating that card’s fault an hour later.

Check the setpoint before the loop: a unit holding a design setpoint through a mild afternoon can miss it for reasons that have nothing to do with the loop (AHU-0023). This rule is only as meaningful as the setpoint it is handed — which is also the caution for any host binding a design constant to sat_sp. Then read the sign, which the rule computes and does not report: consistently warm in a cooling mode points at capacity, authority, or a coil fighting another coil, consistently cold at over-cooling (check AHU-0019), and a miss that changes sign through the day at tuning or hunting (AHU-0022).

Test Vectors

12 scenarios, clock step 300 s over 10800 s.

{
  "schema": "cxf-library/vectors/v1",
  "clock": {
    "step_s": 300,
    "horizon_s": 10800
  },
  "scenarios": [
    {
      "name": "sat_tracks_its_setpoint",
      "description": "Healthy occupied operation: a modulating loop holding 13.2 \u00b0C against a 13.0 \u00b0C setpoint. The 0.2 K residual is ordinary loop error, well inside the 1.7 K band, and no valve position is needed to say so.",
      "inputs": {
        "sat": 13.2,
        "sat_sp": 13.0
      },
      "expect": [
        {
          "output": "yFault",
          "from_s": 0,
          "to_s": 10800,
          "equals": false
        }
      ]
    },
    {
      "name": "mistuned_loop_runs_warm_at_a_part_open_valve",
      "description": "The case this rule exists for: SAT parked 3 K above a 13.0 \u00b0C setpoint with the cooling valve modulating around 60% and never saturating. AHU-0013 is structurally blind to it \u2014 its second conjunct needs the valve above 99% \u2014 and this rule sees it on two temperatures alone. Alarms after the 60 min delay.",
      "inputs": {
        "sat": 16.0,
        "sat_sp": 13.0
      },
      "expect": [
        {
          "output": "yFault",
          "from_s": 0,
          "to_s": 3300,
          "equals": false
        },
        {
          "output": "yFault",
          "from_s": 3900,
          "to_s": 10800,
          "equals": true
        }
      ]
    },
    {
      "name": "mistuned_loop_runs_cold",
      "description": "Same defect with the sign reversed: SAT 2.5 K below setpoint on a loop that never opens its heating valve far enough to trip AHU-0007. Pins the Abs \u2014 without it half the rule's population would be invisible.",
      "inputs": {
        "sat": 10.5,
        "sat_sp": 13.0
      },
      "expect": [
        {
          "output": "yFault",
          "from_s": 0,
          "to_s": 3300,
          "equals": false
        },
        {
          "output": "yFault",
          "from_s": 3900,
          "to_s": 10800,
          "equals": true
        }
      ]
    },
    {
      "name": "edge_positive_gap_at_the_threshold",
      "description": "Strict boundary, clear side. 14.7 \u2212 13.0 is the closest a realistic temperature pair gets to APAR's 1.7 K threshold from below: the difference evaluates to 1.6999999999999993, one ulp under the parameter, and GreaterThreshold is u > t, so it reads healthy.",
      "inputs": {
        "sat": 14.7,
        "sat_sp": 13.0
      },
      "expect": [
        {
          "output": "yFault",
          "from_s": 0,
          "to_s": 10800,
          "equals": false
        }
      ]
    },
    {
      "name": "edge_positive_gap_just_over_the_threshold",
      "description": "Strict boundary, fault side: the same setpoint with SAT 10 mK warmer puts the gap at 1.71 K, which clears u > t and alarms after the delay.",
      "inputs": {
        "sat": 14.71,
        "sat_sp": 13.0
      },
      "expect": [
        {
          "output": "yFault",
          "from_s": 0,
          "to_s": 3300,
          "equals": false
        },
        {
          "output": "yFault",
          "from_s": 3900,
          "to_s": 10800,
          "equals": true
        }
      ]
    },
    {
      "name": "edge_negative_gap_at_the_threshold",
      "description": "Same boundary on the cold side: sat \u2212 sat_sp = \u22121.6999999999999993, |gap| sits on the line and reads healthy. The band is symmetric, so both signs have to be pinned.",
      "inputs": {
        "sat": 13.0,
        "sat_sp": 14.7
      },
      "expect": [
        {
          "output": "yFault",
          "from_s": 0,
          "to_s": 10800,
          "equals": false
        }
      ]
    },
    {
      "name": "edge_negative_gap_just_over_the_threshold",
      "description": "Cold side, fault: sat \u2212 sat_sp = \u22121.71 K. The magnitude clears the threshold and the alarm asserts at the same 10 mK margin the warm side does.",
      "inputs": {
        "sat": 13.0,
        "sat_sp": 14.71
      },
      "expect": [
        {
          "output": "yFault",
          "from_s": 0,
          "to_s": 3300,
          "equals": false
        },
        {
          "output": "yFault",
          "from_s": 3900,
          "to_s": 10800,
          "equals": true
        }
      ]
    },
    {
      "name": "alarm_asserts_exactly_at_the_delay",
      "description": "The TrueDelay edge pinned tick by tick rather than with margin: a 3 K miss present from load, false at 3300 s, true at 3600 s. delayOnInit is true, so a miss already there when the controller restarts waits out the full hour instead of alarming on the first tick.",
      "inputs": {
        "sat": 16.0,
        "sat_sp": 13.0
      },
      "expect": [
        {
          "output": "yFault",
          "from_s": 0,
          "to_s": 3300,
          "equals": false
        },
        {
          "output": "yFault",
          "from_s": 3600,
          "to_s": 10800,
          "equals": true
        }
      ]
    },
    {
      "name": "miss_clears_one_step_before_the_delay_expires",
      "description": "The other side of the same edge: the miss holds from 0 s and ends at 3300 s, one step short of the hour. The timer resets on that tick and nothing is ever reported.",
      "inputs": {
        "sat": [
          {
            "t": 0,
            "value": 16.0
          },
          {
            "t": 3300,
            "value": 13.2
          }
        ],
        "sat_sp": 13.0
      },
      "expect": [
        {
          "output": "yFault",
          "from_s": 0,
          "to_s": 10800,
          "equals": false
        }
      ]
    },
    {
      "name": "setpoint_reset_step_never_alarms",
      "description": "A reset schedule steps the setpoint down 3 K at 600 s and the coil takes 2400 s to catch up \u2014 40 minutes of genuine tracking error caused by nothing but the step. Shorter than the hour, so it stays quiet. This transient is why the ungated form carries a longer delay than AHU-0007 and AHU-0013.",
      "inputs": {
        "sat": [
          {
            "t": 0,
            "value": 16.2
          },
          {
            "t": 3000,
            "value": 13.2
          }
        ],
        "sat_sp": [
          {
            "t": 0,
            "value": 16.0
          },
          {
            "t": 600,
            "value": 13.0
          }
        ]
      },
      "expect": [
        {
          "output": "yFault",
          "from_s": 0,
          "to_s": 10800,
          "equals": false
        }
      ]
    },
    {
      "name": "fault_clears_when_the_loop_is_retuned",
      "description": "A 3 K miss alarms at 3600 s; at 7200 s the loop is corrected and SAT returns to 13.2 \u00b0C. The alarm drops on that tick \u2014 assertion waits out the delay, recovery does not.",
      "inputs": {
        "sat": [
          {
            "t": 0,
            "value": 16.0
          },
          {
            "t": 7200,
            "value": 13.2
          }
        ],
        "sat_sp": 13.0
      },
      "expect": [
        {
          "output": "yFault",
          "from_s": 0,
          "to_s": 3300,
          "equals": false
        },
        {
          "output": "yFault",
          "from_s": 3900,
          "to_s": 6900,
          "equals": true
        },
        {
          "output": "yFault",
          "from_s": 7500,
          "to_s": 10800,
          "equals": false
        }
      ]
    },
    {
      "name": "oscillating_miss_never_alarms",
      "description": "Pins the blind spot persistence buys. SAT swings between 16.0 \u00b0C and 13.2 \u00b0C every 20 minutes against a 13.0 \u00b0C setpoint \u2014 a hunting loop that spends half its day outside the band \u2014 and the timer resets on every compliant tick, so this rule stays silent. AHU-0022 is the rule that reports it.",
      "inputs": {
        "sat": [
          {
            "t": 0,
            "value": 16.0
          },
          {
            "t": 1200,
            "value": 13.2
          },
          {
            "t": 2400,
            "value": 16.0
          },
          {
            "t": 3600,
            "value": 13.2
          },
          {
            "t": 4800,
            "value": 16.0
          },
          {
            "t": 6000,
            "value": 13.2
          },
          {
            "t": 7200,
            "value": 16.0
          },
          {
            "t": 8400,
            "value": 13.2
          },
          {
            "t": 9600,
            "value": 16.0
          }
        ],
        "sat_sp": 13.0
      },
      "expect": [
        {
          "output": "yFault",
          "from_s": 0,
          "to_s": 10800,
          "equals": false
        }
      ]
    }
  ]
}